Goal-based investing with goal postponement: multistage stochastic mixed-integer programming approach

Abstract

This paper introduces a multistage stochastic mixed-integer programming model designed for a goal-based investing (GBI) problem, incorporating the option of goal postponement. Our model allows individuals to defer the fulfillment of their goals within a predefined timeframe. We emphasize the advantages of incorporating goal postponement into the GBI framework, including its ability to accommodate stage-preference ambiguity, address mistiming issues, and enhance utility for individuals. Theoretical results of a GBI problem with goal postponement are presented, and to tackle large-scale multistage GBI problems, we employ a decomposition algorithm known as stochastic dual dynamic integer programming (SDDiP). Numerical results demonstrate that the option to postpone a goal proves especially advantageous when goals are exposed to high inflation rates, and SDDiP emerges as a computationally efficient approach for handling large-scale GBI problems.